Here, we theoretically investigate an alternative way to create an effective magnetic field, considering the states of a harmonic oscillator as an extra spatial dimension. Standard approaches, for instance using a fast rotation of the gas or space-dependent dressing some internal degree of freedom, have not yet achieved effective magnetic fields which are high enough to produce the desired systems. Yet, it is difficult to make them behave in a topologically non trivial manner, for example by embedding them in a strong effective magnetic field. Atoms, for instance, naturally interact between each other. There has been a lot of effort from photonic and atomic platforms to realize such a system. Synthetic matter can help understand intricate systems where interactions compete with other phenomena, such as topological order. The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions In addition, we also use this dissipation to map out the density in and around the transport region, similar to a dissipative scanning gate microscope for ultracold atoms. In this work we characterize how this loss affects transport and develop an extension of the Landauer-Büttiker formalism to include the losses. In the case where there is a near-resonant beam inside the channel, a particle can be transmitted, reflected but also lost due to photon scattering. To model transport between the two reservoirs through an atomic quantum point contact, we typically use the Landauer-Büttiker formalism which identifies transmission and conductance. Quantized conductance through a dissipative atomic point contact This also gives us the possibility to detect minute variations the number of atoms in the channel, seeing the distance between the conductance plateaus being modified by a change of only two particles. This lifts the degeneracy between the two spin states by twice the Fermi energy on a length on the order of the Fermi scale. Although the light is close to resonance, we are able to observe quantized plateaus of conductance after measuring for several seconds without detrimental heating. In this set of experiment, the frequency of the light is tuned to be repulsive for one state and attractive for the other. Quantized conductance through a spin-selective atomic point contact In our set of companion papers, we use a tweezer beam localized inside the 1D wire connecting two reservoirs of a two-component Fermi gas and study both the effect of the internal state, realizing a spin filter, as well as the effect of dissipation on mesoscopic transport. However, unless one uses specific atomic species with narrow transitions, this technique requires close to resonance beam which lead to detrimental heating. Optical manipulation of the internal state is very flexible thanks to beam shaping techniques. Manipulating this internal degree of freedom can be realized magnetically, with radio-frequency fields, or optically using light which will act differentially on the internal states thanks to the vectorial light shift. Ultracold atoms possess both external degrees of freedom which are manipulated by lasers and magnetic fields as well as internal degrees of freedom which are useful to emulate spin physics. Using near-resonant light to manipulate the atoms in a transport geometry This flexibility together with the unique tunability of interactions in lithium enables us to probe quantum cold atomic devices made of correlated matter. Ranging from single obstacles to optical lattices. Using a high-resolution microscope objective and a Digital Micromirror Device we generate almost arbitrary optical potentials for the lithium gas, This allows us to measure conductances of small cold atomic samples, such as two dimensional films and one-dimensional contacts, with direct analogies to quantum electronic devices. We use a two-terminal setup, consisting of two atomic reservoirs smoothly connected by a mesoscopic channel. Welcome to the Lithium lab! Here we study the properties of low temperature gases of fermionic lithium-6. A 25, L939 (1992).Quantum transport of fermions through mesoscopic structures Tarlini, Contractions of Quantum Groups, Springer Lecture Notes in Mathematics, Vol. Majid, Foundations of Quantum Group Theory (Cambridge University Press, Cambridge, 1995). Pressley, A Guide to Quantum Groups (Cambridge University Press, Cambridge, 1994). Connes, Non-commutative Geometry (Academic, London, 1994).
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